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| In ], '''X-waves''' are ]s of the ] that travel at a constant ] in a given direction. X-waves can be ], ], or ]s. They are built as a non-] ] of ]s. Ideal X-waves carry ] ], but finite-energy realizations have been observed in various frameworks. X-wave pulses can have superluminal ] and ].<ref>{{cite journal |title=Measurement of the spatiotemporal electric field of ultrashort superluminal Bessel-X pulses |first1=Pamela |last1=Bowlan |first2=Heli |last2=Valtna-Lukner |display-authors=etal |journal=Optics and Photonics News |page=42 |volume=20 |issue=12 |date=December 2009|doi=10.1364/OPN.20.12.000042 }}</ref> | |||
| In ], '''X-waves''' are ] solutions of the ] that travel at a ] along a given direction. | |||
| ⚫ | In optics, X-waves solution have been reported within a quantum mechanical formulation.<ref>A. Ciattoni and C. Conti, ''arxiv.org'' 0704.0442v1.</ref> | ||
| X-waves can be ], ], or ]s. They are built as a non-] ] of ]s. | |||
| X-waves carry ] ] and travel ]ly (for electromagnetic waves). Finite energy realizations have been observed in various frameworks. | |||
| ⚫ | In optics, X-waves |
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| ⚫ | == References== | ||
| ⚫ | * |
||
| ⚫ | * |
||
| ⚫ | * Various authors in the book edited by |
||
| == See also == | == See also == | ||
| * ] | * ] | ||
| * ] | |||
| ⚫ | == References== | ||
| <references/> | |||
| ⚫ | * J. Lu and J. F. Greenleaf, "Nondiffracting X waves: exact solutions to free-space ] equation and their infinite realizations", ] Trans. Ultrasonic Ferroelectric Frequency. '']'' 39, 19–31 (1992). | ||
| ⚫ | * Erasmo Recami and Michel Zamboni-Rached and Hugo E. Hernandez-Figueroa, "" ''arxiv.org'' 0708.1655v2. | ||
| ⚫ | * Various authors in the book edited by Erasmo Recami, Michel Zamboni-Rached and Hugo E. Hernandez-Figueroa | ||
| ==External links == | ==External links == | ||
| * , a research collaboration devoted to the investigation of X-waves and conical waves in general | * , a research collaboration devoted to the investigation of X-waves and conical waves in general | ||
| * page at the website. | * page at the website. | ||
| ] | ] | ||
| {{ |
{{classicalmechanics-stub}} | ||
Latest revision as of 04:17, 6 January 2025
Not to be confused with X-ray or X-band. | This article may be too technical for most readers to understand. Please help improve it to make it understandable to non-experts, without removing the technical details. (May 2020) (Learn how and when to remove this message) |
In physics, X-waves are localized solutions of the wave equation that travel at a constant velocity in a given direction. X-waves can be sound, electromagnetic, or gravitational waves. They are built as a non-monochromatic superposition of Bessel beams. Ideal X-waves carry infinite energy, but finite-energy realizations have been observed in various frameworks. X-wave pulses can have superluminal phase and group velocity.
In optics, X-waves solution have been reported within a quantum mechanical formulation.
See also
References
- Bowlan, Pamela; Valtna-Lukner, Heli; et al. (December 2009). "Measurement of the spatiotemporal electric field of ultrashort superluminal Bessel-X pulses". Optics and Photonics News. 20 (12): 42. doi:10.1364/OPN.20.12.000042.
- A. Ciattoni and C. Conti, Quantum electromagnetic X-waves arxiv.org 0704.0442v1.
- J. Lu and J. F. Greenleaf, "Nondiffracting X waves: exact solutions to free-space scalar wave equation and their infinite realizations", IEEE Trans. Ultrasonic Ferroelectric Frequency. Control 39, 19–31 (1992).
- Erasmo Recami and Michel Zamboni-Rached and Hugo E. Hernandez-Figueroa, "Localized waves: A scientific and historical introduction" arxiv.org 0708.1655v2.
- Various authors in the book Localized Waves edited by Erasmo Recami, Michel Zamboni-Rached and Hugo E. Hernandez-Figueroa
External links
- The Virtual Institute for Nonlinear Optics (VINO), a research collaboration devoted to the investigation of X-waves and conical waves in general
- Nolinear X-waves page at the nlo.phys.uniroma1.it website.
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